Non-local diffusion with free boundaries

Diego Marcon; Rafayel Teymurazyan

Non-local diffusion with free boundaries

Analysis of PDEs 2025-10-21 v2

Authors: Diego Marcon , Rafayel Teymurazyan

Abstract

We prove optimal regularity and derive several geometric properties for solutions of a free boundary problem with fractional diffusion. Additionally, we deduce local $C^{1,\alpha}$ regularity results for the corresponding interior and exterior free boundaries.

Keywords

free boundary problem nonlinear diffusion equations regularity for elliptic equations

Cite

@article{arxiv.2001.01145,
  title  = {Non-local diffusion with free boundaries},
  author = {Diego Marcon and Rafayel Teymurazyan},
  journal= {arXiv preprint arXiv:2001.01145},
  year   = {2025}
}

Comments

18 pages

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